LollipopE: Bi-centered lollipop embedding for complex logic query on knowledge graph.

Answering complex First-Order Logic (FOL) query plays a vital role in multi-hop knowledge graph (KG) reasoning. Geometric methods have emerged as a promising category of approaches in this context. However, existing best-performing geometric query embedding (QE) model is still up against three-fold potential problems: (i) underutilization of embedding space, (ii) overreliance on angle information, (iii) uncaptured hierarchy structure. To bridge the gap, we propose a lollipop-like bi-centered query embedding method named LollipopE. To fully utilize embedding space, LollipopE employs learnable centroid positions to represent multiple entities distributed along the same axis. To address the potential overreliance on angular metrics, we design an angular-based and centroid-based metric. This involves calculating both an angular distance and a centroid-based geodesic distance, which empowers the model to make more informed selections of relevant answers from a wider perspective. To effectively capture the hierarchical relationships among entities within the KG, we incorporate dynamic moduli, which allows for the representation of the hierarchical structure among entities. Extensive experiments demonstrate that LollipopE surpasses the state-of-the-art geometric methods. Especially, on more hierarchical datasets, LollipopE achieves the most significant improvement.

Tackling higher-order relations and heterogeneity: Dynamic heterogeneous hypergraph network for spatiotemporal activity prediction.

Spatiotemporal activity prediction aims to predict user activities at a particular time and location, which is applicable in city planning, activity recommendations, and other domains. The fundamental endeavor in spatiotemporal activity prediction is to model the intricate interaction patterns among users, locations, time, and activities, which is characterized by higher-order relations and heterogeneity. Recently, graph-based methods have gained popularity due to the advancements in graph neural networks. However, these methods encounter two significant challenges. Firstly, higher-order relations and heterogeneity are not adequately modeled. Secondly, the majority of established methods are designed around the static graph structures that rely solely on co-occurrence relations, which can be imprecise. To overcome these challenges, we propose DyH2N, a dynamic heterogeneous hypergraph network for spatiotemporal activity prediction. Specifically, to enhance the capacity for modeling higher-order relations, hypergraphs are employed in lieu of graphs. Then we propose a set representation learning-inspired heterogeneous hyperedge learning module, which models higher-order relations and heterogeneity in spatiotemporal activity prediction using a non-decomposable manner. To improve the encoding of heterogeneous spatiotemporal activity hyperedges, a knowledge representation-regularized loss is introduced. Moreover, we present a hypergraph structure learning module to update the hypergraph structures dynamically. Our proposed DyH2N model has been extensively tested on four real-world datasets, proving to outperform previous state-of-the-art methods by 5.98% to 27.13%. The effectiveness of all framework components is demonstrated through ablation experiments.